Related papers: A Domain Decomposition Deep Neural Network Method …
Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…
In this paper, a meshfree method using the deep neural network (DNN) approach is developed for solving two kinds of dynamic two-phase interface problems governed by different dynamic partial differential equations on either side of the…
A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces. Since the solution has low regularity across…
We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…
Scientific computing has been an indispensable tool in applied sciences and engineering, where traditional numerical methods are often employed due to their superior accuracy guarantees. However, these methods often encounter challenges…
Deep Neural Networks (DNNs) have already become a crucial computational approach to revealing the spatial patterns in the human brain; however, there are three major shortcomings in utilizing DNNs to detect the spatial patterns in…
Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…
In this paper, a new Discontinuity Capturing Shallow Neural Network (DCSNN) for approximating $d$-dimensional piecewise continuous functions and for solving elliptic interface problems is developed. There are three novel features in the…
The scope of research in the domain of activation functions remains limited and centered around improving the ease of optimization or generalization quality of neural networks (NNs). However, to develop a deeper understanding of deep…
The existence of multiple load-solution mappings of non-convex AC-OPF problems poses a fundamental challenge to deep neural network (DNN) schemes. As the training dataset may contain a mixture of data points corresponding to different…
Avoiding collisions is the core problem in multi-agent navigation. In decentralized settings, when agents have limited communication and sensory capabilities, collisions are typically avoided in a reactive fashion, relying on local…
Multi-agent Pathfinding (MAPF) problem generally asks to find a set of conflict-free paths for a set of agents confined to a graph and is typically solved in a centralized fashion. Conversely, in this work, we investigate the decentralized…
At the heart of neural network force fields (NNFFs) is the architecture of neural networks, where the capacity to model complex interactions is typically enhanced through widening or deepening multilayer perceptrons (MLPs) or by increasing…
In the past, research on a single low dimensional activation function in networks has led to internal covariate shift and gradient deviation problems. A relatively small research area is how to use function combinations to provide property…
A fast method is presented for adaptive moving mesh generation in multi-dimensions using a domain decomposition parabolic Monge-Amp\`ere approach. The domain decomposition procedure employed here is non-iterative and involves splitting the…
In the architecture of deep learning models, inspired by biological neurons, activation functions (AFs) play a pivotal role. They significantly influence the performance of artificial neural networks. By modulating the non-linear properties…
Recent studies have shown that the choice of activation function can significantly affect the performance of deep learning networks. However, the benefits of novel activation functions have been inconsistent and task dependent, and…
Deep learning-based methods deliver state-of-the-art performance for solving inverse problems that arise in computational imaging. These methods can be broadly divided into two groups: (1) learn a network to map measurements to the signal…
Despite the remarkable success of deep learning in pattern recognition, deep network models face the problem of training a large number of parameters. In this paper, we propose and evaluate a novel multi-path wavelet neural network…
In this paper we present a one dimensional second order accurate method to solve Elliptic equations with discontinuous coefficients on an arbitrary interface. Second order accuracy for the first derivative is obtained as well. The method is…